Flux.jl/src/layers/normalisation.jl

"""
    testmode!(m)
    testmode!(m, false)

Put layers like [`Dropout`](@ref) and [`BatchNorm`](@ref) into testing mode
(or back to training mode with `false`).
"""
function testmode!(m, val::Bool=true)
  prefor(x -> _testmode!(x, val), m)
  return m
end

_testmode!(m, test) = nothing

"""
    Dropout(p)

A Dropout layer. For each input, either sets that input to `0` (with probability
`p`) or scales it by `1/(1-p)`. This is used as a regularisation, i.e. it
reduces overfitting during training.

Does nothing to the input once in [`testmode!`](@ref).
"""
mutable struct Dropout{F}
  p::F
  active::Bool
end

function Dropout(p)
  @assert 0 ≤ p ≤ 1
  Dropout{typeof(p)}(p, true)
end

function (a::Dropout)(x)
  a.active || return x
  y = similar(x)
  rand!(y)
  q = 1 - a.p
  @inbounds for i=1:length(y)
    y[i] = y[i] > a.p ? 1 / q : 0
  end
  return y .* x
end

_testmode!(a::Dropout, test) = (a.active = !test)

"""

    LayerNorm(h::Integer)

A [normalisation layer](https://arxiv.org/pdf/1607.06450.pdf) designed to be
used with recurrent hidden states of size `h`. Normalises the mean/stddev of
each input before applying a per-neuron gain/bias.
"""
struct LayerNorm{T}
  diag::Diagonal{T}
end

LayerNorm(h::Integer) =
  LayerNorm(Diagonal(h))

treelike(LayerNorm)

(a::LayerNorm)(x) = a.diag(normalise(x))

function Base.show(io::IO, l::LayerNorm)
  print(io, "LayerNorm(", length(l.diag.α), ")")
end

"""
    BatchNorm(dims...; λ = identity,
              initβ = zeros, initγ = ones, ϵ = 1e-8, momentum = .1)

Batch Normalization Layer for [`Dense`](@ref) or [`Conv`](@ref) layers.

See [Batch Normalization: Accelerating Deep Network Training by Reducing
     Internal Covariate Shift](https://arxiv.org/pdf/1502.03167.pdf)

In the example of MNIST,
in order to normalize the input of other layer,
put the `BatchNorm` layer before activation function.

```julia
m = Chain(
  Dense(28^2, 64),
  BatchNorm(64, λ = relu),
  Dense(64, 10),
  BatchNorm(10),
  softmax)
```
Normalization with convolutional layers is handled similarly.
```julia
m = Chain(
  Conv((2,2), 1=>16),
  BatchNorm(16, λ=relu),
  x -> maxpool(x, (2,2)),
  Conv((2,2), 16=>8),
  BatchNorm(8, λ=relu),
  x -> maxpool(x, (2,2)),
  x -> reshape(x, :, size(x, 4)),
  Dense(288, 10), softmax) |> gpu
```
"""
mutable struct BatchNorm{F,V,N}
  λ::F  # activation function
  β::V  # bias
  γ::V  # scale
  μ     # moving mean
  σ     # moving std
  ϵ::N
  momentum::N
  active::Bool
end

BatchNorm(dims::Integer...; λ = identity,
          initβ = zeros, initγ = ones, ϵ = 1e-8, momentum = .1) =
  BatchNorm(λ, param(initβ(dims)), param(initγ(dims)), 0., 1., ϵ, momentum, true)

function (BN::BatchNorm)(x)
  λ, γ, β = BN.λ, BN.γ, BN.β
  dims = length(size(x))
  channels = size(x, dims-1)
  affine_shape = ones(Int, dims)
  affine_shape[end-1] = channels
  m = prod(size(x)[1:end-2]) * size(x)[end]

  if !BN.active
    μ = BN.μ
    σ = BN.σ
  else
    T = eltype(x)

    ϵ = data(convert(T, BN.ϵ))
    axes = [1:dims-2; dims] # axes to reduce along (all but channels axis)
    μ = mean(x, axes)
    σ = sqrt.(mean((x .- μ).^2, axes) .+ ϵ)

    # update moving mean/std
    mtm = data(convert(T, BN.momentum))
    BN.μ = (1 - mtm) .* BN.μ .+ mtm .* data(μ)
    BN.σ = (1 - mtm) .* BN.σ .+ mtm .* data(σ) .* m ./ (m - 1)
  end

  λ.(reshape(γ, affine_shape...) .* ((x .- μ) ./ σ) .+ reshape(β, affine_shape...))
end

children(BN::BatchNorm) =
  (BN.λ, BN.β, BN.γ, BN.μ, BN.σ, BN.momentum, BN.ϵ, BN.active)

mapchildren(f, BN::BatchNorm) =  # e.g. mapchildren(cu, BN)
  BatchNorm(BN.λ, f(BN.β), f(BN.γ), BN.μ, BN.σ, BN.momentum, BN.ϵ, BN.active)

_testmode!(BN::BatchNorm, test) = (BN.active = !test)

function Base.show(io::IO, l::BatchNorm)
  print(io, "BatchNorm($(join(size(l.β), ", "))")
  (l.λ == identity) || print(io, ", λ = $(l.λ)")
  print(io, ")")
end